Abstract
We introduce the notion of Hitchin variety over C. Let L be a holomorphic line bundle over a Hitchin variety X. We investigate the space of all global sections of sheaf of differential operators Dk(L) and symmetric powers of sheaf of first order differential operators Sk(D1(L)) over X and show that for a projective Hithcin variety both the spaces are one dimensional. As an application, we show that the space C(L) of holomorphic connections on L does not admit any non-constant regular function.
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